Torque Saturation in Bipedal Robotic Walking through Control Lyapunov Function Based Quadratic Programs

This paper presents a novel method for directly incorporating user-defined control input saturations into the calculation of a control Lyapunov function (CLF)-based walking controller for a biped robot. Previous work by the authors has demonstrated the effectiveness of CLF controllers for stabilizing periodic gaits for biped walkers, and the current work expands on those results by providing a more effective means for handling control saturations. The new approach, based on a convex optimization routine running at a 1 kHz control update rate, is useful not only for handling torque saturations but also for incorporating a whole family of user-defined constraints into the online computation of a CLF controller. The paper concludes with an experimental implementation of the main results on the bipedal robot MABEL

Sugar beet investigations in Ohio in 1900

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Solving the time-dependent Schr\"odinger equation with absorbing boundary conditions and source terms in Mathematica 6.0

In recent decades a lot of research has been done on the numerical solution of the time-dependent Schr\"odinger equation. On the one hand, some of the proposed numerical methods do not need any kind of matrix inversion, but source terms cannot be easily implemented into this schemes; on the other, some methods involving matrix inversion can implement source terms in a natural way, but are not easy to implement into some computational software programs widely used by non-experts in programming (e.g. Mathematica). We present a simple method to solve the time-dependent Schr\"odinger equation by using a standard Crank-Nicholson method together with a Cayley's form for the finite-difference representation of evolution operator. Here, such standard numerical scheme has been simplified by inverting analytically the matrix of the evolution operator in position representation. The analytical inversion of the N x N matrix let us easily and fully implement the numerical method, with or without source terms, into Mathematica or even into any numerical computing language or computational software used for scientific computing.Comment: 15 pages, 7 figure

Role of material properties and mesostructure on dynamic deformation and shear instability in Al-W granular composites

Dynamic experiments with Al-W granular/porous composites revealed qualitatively different behavior with respect to shear localization depending on bonding between Al particles. Two-dimensional numerical modeling was used to explore the mesomechanics of the large strain dynamic deformation in Al-W granular/porous composites and explain the experimentally observed differences in shear localization between composites with various mesostructures. Specifically, the bonding between the Al particles, the porosity, the roles of the relative particle sizes of Al and W, the arrangements of the W particles, and the material properties of Al were investigated using numerical calculations. It was demonstrated in simulations that the bonding between the "soft" Al particles facilitated shear localization as seen in the experiments. Numerical calculations and experiments revealed that the mechanism of the shear localization in granular composites is mainly due to the local high strain flow of "soft" Al around the "rigid" W particles causing localized damage accumulation and subsequent growth of the meso/macro shear bands/cracks. The "rigid" W particles were the major geometrical factor determining the initiation and propagation of "kinked" shear bands in the matrix of "soft" Al particles, leaving some areas free of extensive plastic deformation as observed in experiments and numerical calculations.Comment: 10 pages, 14 figures, submitted to Journal of Applied Physic

World law

In the third millennium of the Christian era, which is characterised by the emergence of a world economy and eventually a world society, the concept of world law is needed to embrace not only the traditional disciplines of public international law, and comparative law, but also the common underlying legal principles applicable in world trade, world finance, transnational transfer of technology and other fields of world economic law, as well as in such emerging fields as the protection of the world's environment and the protection of universal human rights. World law combines inter-state law with the common law of humanity and the customary law of various world communities

System Identification and Control of Valkyrie through SVA--Based Regressor Computation

This paper demonstrates simultaneous identification and control of the humanoid robot, Valkyrie, utilizing Spatial Vector Algebra (SVA). In particular, the inertia, Coriolis-centrifugal and gravity terms for the dynamics of a robot are computed using spatial inertia tensors. With the assumption that the link lengths or the distance between the joint axes are accurately known, it will be shown that inertial properties of a robot can be directly evaluated from the inertia tensor. An algorithm is proposed to evaluate the regressor, yielding a run time of O(n^2). The efficiency of this algorithm yields a means for online system identification via the SVA--based regressor and, as a byproduct, a method for accurate model-based control. Experimental validation of the proposed method is provided through its implementation in three case studies: offline identification of a double pendulum and a 4-DOF robotic leg, and online identification and control of a 4-DOF robotic arm